Technically, it’s been more than a year that the glioblastoma has been in my brain. But then, I didn’t actually get the tumor pathology (hence, I didn’t know it was glioblastoma) until later in April last year. Accordingly, I have no idea exactly how long I’ve been living with glioblastoma. Brain cancer is hard.
Regardless, one year ago today I woke up alone on my kitchen floor with no idea how I got there. Also, I was drooling a little (if you must know). So, April 9 is a date that will be forever burned into my brain. It’s extra-special-super-not-awesome that big R’s birthday is April 4 and little R’s birthday is April 10. Brain cancer has impeccable timing, apparently.
The times, they are a-changin’…
Weeks before the big seizure I never could have imagined my life would change so suddenly. And just weeks ago, I wouldn’t have imagined being where I currently am now – social distancing, teaching from home, homeschooling a first-grader, and wondering just how compromised my immune system really is. On the other hand, accepting my cancer diagnosis and its miserable prognosis mean I feel pretty well-prepared for these uncertain times. One thing is clear: 2019 and 2020 will both be ones for the books.
Since it’s been a year, I have an MRI coming up tomorrow. And, apparently, they haven’t figured out how to do those over Zoom yet. This one comes with a little more scanxiety than usual. In the last months, I’ve had a few “micro-seizure” episodes and headaches with increasing frequency. Naturally, my mind goes to the worst place – recurrence. In actuality, it could be anything including healing from radiation damage. I am hopeful that this one will come back with no evidence of disease (NED), but I’m prepared for other possibilities.
Finding hope in Bayes’ Theorem
A recent tweet from my colleague, Allen Downey, reminded me of the helpfulness of conditional probability – the idea that knowledge of prior events can help better predict future events. Specifically, Bayes’ theorem:
Right about now, I can hear you saying “Hey, nerd! I don’t read this blog to learn math.” (Actually, why do you read this blog? I digress…) But, this is cool. The formula above says the likelihood that statement A is true given that I know B is true is equal to the likelihood that B is true given that I know A is true times the likelihood of A being true divided by the likelihood of B being true.
Let’s do an example so you can see why I’m so psyched about conditional probability. (Caveat emptor: humans are not statistics and there are many complicated factors that influence outcomes. The following example is simplified for illustrative purposes.)
The one-year survival rate for GBM in adults is approximately 25%. The two-year rate is approximately 10%. So, what is the probability that I will survive two years given that I’ve already survived one?
Let’s take that P(B |A) term first. That’s the probability that I’ll survive one year, given that I’ve survived 2. That’s a weird hypothetical, but clearly its value has to be 100% or 1. The P(B) term is the probability of living one year or 0.25. Finally the P(A) term is the probability of surviving two years or 0.10. So now, if we substitute those into the above equation, we get:
The expression above evaluates to 0.4 or 40%! Four times better than just the two-year survival rate? What magic is this!? Well, here’s one way to think about it: everyone who dies before making it a year, also dies before making it to two years. Then a bunch more people die between years one and two. That’s why the two-year survival rate is lower than the one-year rate. So, when we do the conditional probability, we are “factoring in” our prior knowledge that someone has survived one year (or conversely, factoring out the folks who died within a year from the computation of the two-year survival rate).
Long story short, Bayes’ Theorem predicts that every year I survive makes it more likely that I’ll survive to the next milestone. Of course, we reach diminishing returns as the survival rates for subsequent milestones get smaller, but for now, I like my (conditional) odds!